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%I #13 Mar 18 2017 09:54:19
%S 3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,
%T 1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,
%U 1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4
%N "Plain Bob Minimus" in bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 3 in n-th permutation.
%H David Joyner, <a href="http://www.usna.edu/Users/math/wdj/book/node158.html">Application: Bell Ringing</a>
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1).
%H <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>
%F Period 24.
%F From _Chai Wah Wu_, Jul 17 2016: (Start)
%F a(n) = a(n-1) - a(n-4) + a(n-5) - a(n-8) + a(n-9) - a(n-12) + a(n-13) - a(n-16) + a(n-17) - a(n-20) + a(n-21) for n > 21.
%F G.f.: x*(-4*x^20 + x^19 + x^18 + x^17 - 4*x^16 - 3*x^12 - x^11 + x^9 - 2*x^8 - 2*x^4 + x^3 - x - 3)/((x - 1)*(x^4 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^8 - x^4 + 1)). (End)
%Y Cf. A090277-A090284.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jan 24 2004
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